Hyperspherical phase synchrony for quantifying multivariate phase synchronization

Time-varying phase synchrony is an important bivariate measure that quantifies both linear and nonlinear dynamics between non-stationary signals. Recently, multivariate phase synchronization has been proposed to investigate the interactions within a group of oscillators. However, current approaches are limited to either averaging all pairwise synchrony values, which causes a loss of information, or forming a matrix of bivariate synchronization indices, where the distribution of the eigenvalues is exploited to estimate the multivariate synchrony. None of these methods is a direct way to quantify the multivariate synchrony since they use bivariate synchrony values to estimate the group dynamics. Therefore, the reliability of these measures is affected by the accuracy of the bivariate synchrony estimates. In this paper, a novel and direct method of computing the multivariate phase synchrony is proposed. The performance of the new estimator is evaluated through simulations showing the effectiveness of the new measure compared to existing methods.